Biasing in MOSFET Amplifiers

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Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing in MOSFET Amplifiers

• Biasing: Creating the circuit to establish the desired DC voltages and currents for the operation of the amplifier

• Four common ways:

1. Biasing by fixing VGS

2. Biasing by fixing VG and connecting a resistance in the Source 3. Biasing using a Drain-to-Gate Feedback Resistor 4. Biasing Using a Constant-Current Source

MOSFETs 1 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing in MOSFET Amplifiers V • Biasing by fixing VGS DD

W 2 1 RD I D = kn′ ()VGS −Vt V 2 GG VG L V ε R D k′ = μ ox = μ C G n n n ox M1 tox

-VEE When the MOSFET device is changed (even using the same supplier), this method can result in a large variability in the value of

ID. Devices 1 and 2 represent extremes among units of the same type. MOSFETs 2 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing in MOSFET Amplifiers

• Biasing by fixing VG and connecting a resistance in the Source

Degeneration Resistance

MOSFETs 3 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing in MOSFET Amplifiers • Biasing using a Drain-to-Gate Feedback Resistor

Large Resistor

MOSFETs 4 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing in MOSFET Amplifiers • Biasing Using a Constant-Current Source

Current Mirror

Used in Integrated Circuits

Figure 4.33 (a) Biasing the MOSFET using a constant-current source I. (b) Implementation of the constant-current source I using a current mirror.

MOSFETs 5 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Current Mirror DC Analysis • The width and length (the W/L aspect ratio) and the parameters of the two transistors can be different • We can choose W/L freely • In this circuit, consider W/L of both MOSFETs are the same and transistors I are identical. The Gate-Source voltages W1 are also the same, then W1 L1 L1 1 W1 2 + + I REF = 2 kn′ ()VGS −Vt L1 VGS VGS 1 W1 2 I = k′ ()V −V I W1 L1 - - 2 n GS t = ⋅ =1 L1 I REF L1 W1

I = I REF MOSFETs 6 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Current Mirror DC Analysis

• Designing IREF

V −V +V I = DD GS SS REF R

1 W1 2 I REF = 2 kn′ ()VGS −Vt L1

• It is often needed to find the value of R in order to achieve a desired IREF

MOSFETs 7 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Biasing of MOSFET Amplifier

• 1- Intro to MOS Field Effect Transistor (MOSFET) • 2- NMOS FET • 3- PMOS FET • 4- DC Analysis of MOSFET Circuits • 5- MOSFET Amplifier • 6- MOSFET Small Signal Model • 7- MOSFET Integrated Circuits • 8- CSA, CGA, CDA • 9- CMOS Inverter & MOS Digital Logic

MOSFETs 8 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I MOSFET Design Space • Modern integrated circuits use MOSFETs extensively – Very high densities of transistors – up to 109 transistors/cm2 in some ULSI memory arrays. – Off-chip discrete resistors and capacitors are NOT commonly used – On-chip resistors and capacitors generally small – Multistage amplifiers are usually DC-coupled • Transistors used wherever possible to implement current sources, resistors, capacitors,

MOSFETs 9 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Using MOSFETs to implement R’s and C’s

• Resistors: Active Loads (large R’s) Diode-connected loads (small R’s) MOSFET Triode-Region (moderate R’s) • Capacitors Most obvious is the gate-body capacitor Can be used to have variable-capacitors as well • Current Mirrors

MOSFETs 10 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I MOSFET Active Loads • MOSFETs used as an active load for high resistances: – MOSFET is held in saturation with the source and gate held at a constant DC voltage 1 – Drain connected to circuit ro = λ ⋅ I D –ro is inversely proportional to ID

vgs = 0 Rin=ro gmvgs = 0

Rin= ? MOSFETs 11 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Diode-Connected MOSFETs • A Diode connected MOSFET can be used to achieve small resistances: – The Drain is directly connected to Gate, and therefore it can only be operated in saturation (or cutoff)

Source Absorption Theorem

MOSFETs 12 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I MOSFET Current Mirrors • Used extensively in MOSFET IC applications

•Often ro,is neglected. Since there is no gate current, the drain currents of M1 and M2 are identical VX I 00 • In practice, IREF ≠ I due to finite ro. (Not included in EC1) + + 1 W V V ′ 1 2 GS GS I REF = kn ()VX −Vt (1+ λVX ) - - 2 L1

VX = VGS1 = VDS1 The current I will also depend on VDS2 MOSFETs 13 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Current Mirror DC Analysis • The width and length (the W/L aspect ratio) of MOSFETs can be designed almost freely • Since the W/L of M1 and M2 need not be the same, the size I ratios can affect current ratios W W W 1 2 I = 1 k′ 1 ()V −V 2 L L REF 2 n L GS t 1 2 1 + + 1 W2 2 VGS VGS I = 2 kn′ ()VGS −Vt L2 - - I W L = 2 ⋅ 1 I REF L2 W1 MOSFETs 14 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Current Scaling (Steering) • Ratio of aspect ratios can be selected to achieve W W W W nearly any L L L L scale factor I/IREF

Note: All gates are connected

MOSFETs 15 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Current Mirroring – Pushing and Pulling

MOSFETs 16 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Small Signal • Transistor M1 is diode connected and acts like a resistor to s.-s. ground.

ro2

MOSFETs 17 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Outline of Chapter 5

MOSFETs 18 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I DC and AC - Body-Effect / CLM Three types of analysis: Neglect DC Body-Effect & DC CLM Use DC Body-Effect / Neglect DC CLM DC Analysis Use DC Body-Effect / Use DC CLM Use whatever DC values for V and I in the small-signal Three types of analysis: analysis Neglect AC Body-Effect & AC CLM AC Analysis Use AC Body-Effect / Neglect AC CLM (small-signal) Use AC Body-Effect / Use CLM

MOSFETs 19 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Common Source Amplifier (CSA)

• Current source I implemented with current mirror. • Current mirror provides active load at drain • Source terminal grounded – no DC or AC Body effect

MOSFETs 20 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CSA with Current Mirror

ro2 CSA

MOSFETs 21 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CSA Small Signal Analysis • From MOSFET Current-Mirror: only ro2 appears in analysis

vgs1 = vi

vout = −gm1(ro1 ro2 )vgs1

vout AV = = −gm1()ro1 ro2 vi

MOSFETs 22 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CSA Input/Output Resistance

• Input Resistance

RIN ⇒ ∞ • Output resistance

vgs1 = 0

gm1vgs1 = 0

ROUT = ro1 ro2

MOSFETs 23 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CSA Calculations • In practice, difficult to keep all transistors operating in saturation

VOUT is hard to control, and sensitive to: W/L, VG, and CLM λ λ = = 0.01V −1 1 2 Hand: SPICE:

Vt1 = Vt 2 =1V VG = 2.567V VG = 2.58V μ A k′p = 50 V I = 2.596mA I = 2.57mA k′ =125μ A n V VOUT = 3.855V VOUT = 2.895V A V W2 W1 g = 5.192m A = −102.4 = 50, = 40 m1 V V V L2 L1 ro = 38.52kΩ

VDD = 5V ,VSS = −2V V AV = −100 V

RREF =1kΩ

MOSFETs 24 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I Common Gate Amplifier (CGA) • A pMOS current mirror is used as IREF including the output resistance. • The gate terminal held at a DC voltage. (AC Ground) • Since source terminal not at signal ground, the body effect is present. Typically used as second stage of a multi-stage amplifier circuit

MOSFETs 25 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CGA – DC Analysis • Current mirror is assumed to be ideal during the DC analysis, thus IREF=I

• DC voltage at the source terminal (VS) must be obtained from driving the current IREF through the transistor. • This assumes that the input voltage source VI is set to zero

•RI is part of the source voltage

• Solve for VO, with VS and VG known, and including CLM W I = 1 k′ ()()V −V −V 2 []1+ λ ⋅ V −V 2 n L G S t O S MOSFETs 26 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CGA

• Replace with a current source including output resistance ro2

ro2

Choice of analysis:

Neglect AC Body-Effect & CLM

Use AC Body-Effect / Neglect CLM

Use AC Body-Effect / Use CLM

MOSFETs 27 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CGA – No Body Effect or CLM

vo = −gmvgs ⋅ ro2 i=0 1 g v = − m1 v gs 1 I + RI gm1

vo ro2 AV = = Non Inverting vI 1 + RI gm

MOSFETs 28 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I

CGA – RIN & ROUT, No Body Effect or CLM

1 RIN = gm1

ROUT

vI = 0

RIN

ROUT = ro2

MOSFETs 29 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CGA – With Body Effect & no CLM

Solve at vx first:

vbs1 = vgs1 = −vx vX RIN

vo = −(gm1vgs1 + gmb1vbs1 )ro2

vo = −(gm1vx + gmb1vx )ro2

vo AV = = ()gm1 + gmb1 ro2 vx Include RI and v v v R solve for total A = o = o ⋅ x = ()g + g r ⋅ IN voltage gain in V −total m mb o 2 vi v x vi RIN + RI term of RIN MOSFETs 30 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I

CGA – RIN With Body Effect & no CLM iX

vX vbs1 = vgs1 = −vx RIN iIN ix = (gm1 + gmb1)vx

iin = (gm1 + gmb1)vx

1 Neglect Input R = IN g + g Voltage Source m1 mb1

MOSFETs 31 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I CGA - With Body Effect & CLM

iX vx = −vgs

vo = ix ⋅ ro2 vX iX vx − vo ix = ()g m1 + g mb1 vx + Neglect Input ro1

Voltage Source vo ⎛ 1 ⎞ AV = = ()ro1 ro2 ⋅⎜ + gm1 + gmb1 ⎟ vx ⎝ ro1 ⎠

MOSFETs 32 Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I

CGA – RIN With Body Effect & CLM iX

vX RIN vo = ix ⋅ ro2

vx − vo ix = ()gm1 + gmb1 vx + ro1 r 1+ o2 vx ro1 Neglect Input RIN = = ix 1 Voltage Source + gm1 + gmb1 ro1

MOSFETs 33